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Find values for a and b that make the statement true.

a plus b i equals 7 plus 5 i
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Part 1
aequals
  
enter your response here ​(Simplify your​ answer.)
Part 2
bequals
  
enter your response here ​(Simplify your​ answer.)

1 answer

To solve the equation \( a + bi = 7 + 5i \), we need to match the real parts and the imaginary parts on both sides of the equation.

  1. Real parts: The real part of the left side is \( a \) and the real part of the right side is \( 7 \). Therefore, \[ a = 7 \]

  2. Imaginary parts: The imaginary part of the left side is \( b \) and the imaginary part of the right side is \( 5 \). Therefore, \[ b = 5 \]

Thus, the values are:

  • Part 1: \( a = 7 \)
  • Part 2: \( b = 5 \)

So, you can enter:

  • Part 1: \( a = 7 \)
  • Part 2: \( b = 5 \)